Question: Geometry of the bivariate normal distribution. Suppose C D v1 c c v2 is positive definite, and let 0;C be the density of

Geometry of the bivariate normal distribution. Suppose C D

 v1 c c v2



is positive definite, and let 0;C be the density of the corresponding bivariate centred normal distribution. Show the following.

(a) The contour lines ¹x 2 R2 W 0;C.x/ D hº for 0 < h < .2

p det C /1 are ellipses.

Determine the principal axes.

(b) The sections R 3 t ! 0;C.a C tb/ with a; b 2 R2; b ¤ 0 are proportional to onedimensional normal densities m;v with suitable m; v.

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